Continuous phase modulation (CPM) signals are phase-modulated signals having a spectral occupancy that can be tailored to fit limited transmission bandwidths through suitable pre-modulation filtering. Moreover, unlike non-constant envelope signals, such as amplitude-modulated signals or filtered phase-modulated signals, the CPM signals have a constant envelope and allow saturated power amplifier operation for maximum power efficiency. These desirable signal properties, desirable by the rising premium being placed on bandwidth and power efficiency, have resulted in the use of CPM signals, such as binary Gaussian Minimum Shift Keying (GMSK) being deployed in operational terrestrial and satellite communication systems.
Inventors Gee L. Lui and Kuang Tsai taught precoding in a low complexity CPM serial demodulator in “Viterbi and Serial Demodulators for Precoded Binary GMSK”, on pp. 676-683, ITC Proceedings, Las Vegas, Nev., 1999. The low complexity CPM serial demodulator operated in combination with the binary CPM GMSK modulator. The binary CPM GMSK modulator received a serial bit data stream that was precoded into a symbol steam by a precoder. The symbols were then modulated by a binary CPM GMSK modulator having a L=1/BT memory length with a modulation index h of ½, where B is the modulation bandwidth and T is the symbol time. The low complexity serial demodulator was described in terms of reduced complexity. The use of data precoding by the precoder in the transmitter enables data decisions by the serial demodulator to be simply made by alternately sampling the sign, using a sampler and a threshold, of the inphase and quadrature components at the output of a phase amplitude modulated (PAM) matched-filter h0(−t). The PAM matched filter filtered the fundamental Laurent components embedded in the received CPM signal.
The advantages of the serial demodulator are its simplicity as well as the ease of generating metrics for soft decision decoding. The decoding metrics were obtained by directly quantizing, into the required number of bits, the respective inphase or quadrature components of the PAM filter output at sampling instances. The disadvantage of the serial demodulator is that its performance may be severely limited by inter-symbol interference (ISI), particularly for small bandwidth-time (BT) products.
To mitigate the problem of ISI, an equalizer was used. ISI refers to the spreading of a data pulse over several bit intervals. ISI is an inherent characteristic of a smooth and spectrally compact modulation waveform, such as GMSK, and a direct consequence of the reciprocal spreading theorem of the Fourier transform, which states that a pulse that is long in time is necessarily narrow in frequency, and vice versa. For a CPM GMSK signal, each data pulse is spread among the set of Q=2L-1 Laurent pulses with pulse periods ranging from (L+1)T for the dominant Laurent component h0(t) to T for the weakest Laurent component. Upon reaching the detection filter of the serial demodulator, these Laurent pulses are further spread by the detection filter h0(−t) resulting in a total data pulse spread as large as 2(L+1) bit periods. Because the autocorrelation function of h0(t) vanishes at ±(L+1)T, a signal sample taken at bit time nT is corrupted by L preceding data bits as well as L succeeding data bits, resulting in ISI, where n is the symbol index. The presence of ISI in the signal sample causes the signal to randomly deviate from its expected value and could greatly impair the decision ability to make correct bit decisions, even in the absence of receiver noise. The effect of ISI on bit detection is generally data pattern dependent and can be effectively mitigated using a least mean square (LMS) equalizer, which operates to minimize the square of the error of the signal sample from the expected value. A LMS equalizer, also known as a transversal equalizer, can be implemented using a tap delay line, a set of multipliers and a multiple-input summer. For BT values of ⅓ to ⅙, it was determined that no more than three taps are needed in each case to provide a near-optimal performance of the LMS equalizers. For BT values of ½ and greater and over the bit SNR range of 0 dB to 10 dB, the performance of the serial demodulator, without an equalizer, is nearly the same as coherent BPSK performance, and thus, equalization is deemed unnecessary for these larger BT values.
The CPM GMSK modulator operation is defined by the bandwidth-time products BT, a modulation index h, and the symbol time period T. A Gaussian modulation filter has a memory length L where L=1/BT. The equalizer is used to solve the problem of high ISI for low BTs. However, the modulation index h presents further detection problems when the value of h is low. Small modulation index partial response precoded binary CPM signals have very narrow bandwidth occupancy and are attractive modulation indexes for use in the design of high-capacity and bandwidth-limited communication systems. However, conventional detection of these narrow-band modulation signals is complex and entails a high complexity data demodulator. Small modulation index partial-response CPM signals are very bandwidth efficient but difficult and complex to demodulate using conventional linear receivers. These and other disadvantages are solved or reduced using the invention.